This is a question of exhuast gas scavenging efficiency. Effective scavenging is an extremely important factor to consider in maximizing your engine's volumetric efficiency, or "V.E." Although the most thorough answer is one that takes far too long to put in this post, Ill give you the shortened one.
Long tube headers are headers where your primary tubes are on average, at least 28" in length, they are also much more narrow that their short tube counter parts. These type of headers, generally speaking, are best when used on a street rod, or "smoke show" application. Basically, lighting up the tires from stoplight to stoplight, generally with a mid to low power band. This is because of the way the engine breathes at mid and lower RPM's.
At the low to mid end, the best way to maximize your scavenging effect, thus helping to maximize your engine's V.E., Is to move the exhuast out of the engine as fast as possible, or with as much velocity as possible. Long tubes work best for this because of their length, and their width (well, lack of width). Thier length allows an elongated path for the gas to flow, thus allowing the gas to leave the cylinder with more speed because the gas has more time to gain velocity before it hits the collector.
Now, you've heard car enthusiasts state that ANY restriction is bad for a motor, no matter what. This is not completely true, in your exhaust, small, strategically placed, smooth mandrel restrictions can be a good thing due to the fact that well place, correct sized restrictions followed by larger openings actually speed up exhuast gas flow. So the smaller diameter tubes actually serve your scavenging better in the mid and low ranges.
Mid and low ranges don't produce a lot of actual exhuast volume, so small tubes don't restrict or "back up" flow.
LARGE, SHORT TUBE HEADERS MAKE FOR "LAZY" EXHUAST GAS SPEED WHEN EXHUAST VOLUME IS LOW! (as it is in the low and mid range).
However, if you don't even begin to tip into your power band until about 3700, you may consider short tubes. High RPM operation in a big motor (not talking about 4 bangers here), yeild LARGE amounts of exhuast gas discharge. THIS is where you need the larger diameter tubes, to get more volume out of the cylinder. THIS is where you can loose power due to pumping losses on the exhuast stroke. In an ideal world, your exhuast system would be soooo effective, that by the time that pistion STARTS coming up on the exhuast stroke, your ports and headers will have scavenged all exhuast gas out of the cylinder during the duration of the exhuast pulse. If there's no sizable amount to push out, there in a low pressure area in the cylinder (also known as vacuum), almost causing a "pulling up" affect on the piston. So, your not loosing power by pushing, your gaining power by being pulled.
Hope this helped!